Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools and Colleges |
From inside the book
Results 1-5 of 100
Page v
... of factoring numbers . Factoring of Algebraic quantities GREATEST COMMON DIVISOR . LEAST COMMON MULTIPLE 128 78 79 80 81 82 83 85 86 87 88 95 96-108 109-113 Definitions - CHAPTER III . ALGEBRAIC FRACTIONS . - Proposition.
... of factoring numbers . Factoring of Algebraic quantities GREATEST COMMON DIVISOR . LEAST COMMON MULTIPLE 128 78 79 80 81 82 83 85 86 87 88 95 96-108 109-113 Definitions - CHAPTER III . ALGEBRAIC FRACTIONS . - Proposition.
Page vi
... Fraction to an Entire or Mixed quantity . To reduce a Mixed quantity to the form of a Fraction 121 122 Signs of Fractions .... 123 To reduce Fractions to a Common Denominator ... 126 To reduce a quantity to a Fraction with a given ...
... Fraction to an Entire or Mixed quantity . To reduce a Mixed quantity to the form of a Fraction 121 122 Signs of Fractions .... 123 To reduce Fractions to a Common Denominator ... 126 To reduce a quantity to a Fraction with a given ...
Page vii
... Fractions 172 .173-177 Perfect and Imperfect Squares - Theorem ..178-179 Approximate Square Roots ...... 180 Square ... Fraction containing Radicals .... 206 Powers and Roots of Radicals ... 207-208 Imaginary or Impossible Quantities ...
... Fractions 172 .173-177 Perfect and Imperfect Squares - Theorem ..178-179 Approximate Square Roots ...... 180 Square ... Fraction containing Radicals .... 206 Powers and Roots of Radicals ... 207-208 Imaginary or Impossible Quantities ...
Page ix
... FRACTIONS - LOGARITHMS - EX- PONENTIAL EQUATIONS INTER- EST AND ANNUITIES . CONTINUED FRACTIONS .. .347-356 LOGARITHMS - Definitions - Characteristic . .357-358 Logarithms of numbers from 1 to 100 359 General Properties of Logarithms ...
... FRACTIONS - LOGARITHMS - EX- PONENTIAL EQUATIONS INTER- EST AND ANNUITIES . CONTINUED FRACTIONS .. .347-356 LOGARITHMS - Definitions - Characteristic . .357-358 Logarithms of numbers from 1 to 100 359 General Properties of Logarithms ...
Page 13
... fraction . Thus , ab , or signifies that a is to be divided by b . a b Division is also represented thus , ab , where a denotes the dividend , and b the divisor . ART . 17. The sign > , is termed the sign of inequality . It denotes that ...
... fraction . Thus , ab , or signifies that a is to be divided by b . a b Division is also represented thus , ab , where a denotes the dividend , and b the divisor . ART . 17. The sign > , is termed the sign of inequality . It denotes that ...
Contents
67 | |
74 | |
80 | |
88 | |
95 | |
105 | |
112 | |
121 | |
123 | |
130 | |
137 | |
148 | |
155 | |
205 | |
211 | |
217 | |
224 | |
227 | |
287 | |
292 | |
293 | |
300 | |
302 | |
316 | |
322 | |
331 | |
337 | |
349 | |
355 | |
362 | |
368 | |
374 | |
384 | |
385 | |
394 | |
Other editions - View all
Common terms and phrases
algebraic algebraic quantity arithmetical progression Binomial Theorem coëfficient continued fraction converging fraction cube root denominator denotes dividend divisible equa equal equation whose roots evident exactly divide EXAMPLES FOR PRACTICE exponent expressed extract the square Find the cube Find the greatest Find the number Find the square Find the sum find the value geometrical progression given number gives greater greatest common divisor Hence least common multiple less letters logarithm method minus monomial Multiply nth root nth term number of balls number of permutations number of terms operation perfect square polynomial positive root preceding proportion proposed equation quotient ratio real roots reduced remainder Required the numbers required to find result second degree second term square root Sturm's theorem substitute subtracted taken theorem third tion transformed transposing unknown quantity whence whole number zero
Popular passages
Page 83 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.
Page 42 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 39 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 128 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 43 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Page 35 - Obtain the exponent of each literal factor in the quotient by subtracting the exponent of each letter in the divisor from the exponent of the same letter in the dividend; Determine the sign of the result by the rule that like signs give plus, and unlike signs give minus.
Page 140 - ... and to the remainder bring down the next period for a dividend. 3. Place the double of the root already found, on the left hand of the dividend for a divisor. 4. Seek how often the divisor is contained...
Page 220 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the lesser, is equal to 12 ? Ans.
Page 183 - Since the square of a binomial is equal to the square of the first term, plus twice the product of the first term by the second, plus the square of the second...
Page 28 - Multiply the coefficients of the two terms together, and to their product annex all the letters in both quantities, giving to each letter an exponent equal to the sum of its exponents in the two factors.